two column angle proofs

Question

GIVEN-Angle 1and angle 2 form a linear pair

Measurement of angle 2 + measurement of angle 3 + measurement of angle 4 = 180

 

PROVE-measurement of angle 1 = measurement of angle 3 + measurement of angle 4 

Answer 1

Hello Brittany,

What they want you to prove is the measure of angle 1= measure of angle 3+measure of angle 4

 

Our given information is angle 1 and angle 2 are a linear pair

and

measure of angle 2+ measure of angle 3 + measure of angle 4 = 180

 

So lets start:

the definition of a linear pair means that angle 1 and 2 equal 180 degrees. (they are adjacent angles and always equal 180 degrees).

Now thinking to measure of angle 2 plus 3 plus 4 equals 180 as our other "given" information.

we could make 2 equations to show our given information:

 

angle 2 + angle 1= 180

 

angle 2+ angle3 +angle 4 = 180

 

To prove that angle 1 is equal to angle 3+angle 4 we need to prove they have the same sum

 

so our first equation:

angle 2 + angle 1= 180

lets move angle 2 over so we have a "value" for angle 1

subtract angle 2 from each side to get:

angle 1= 180 - angle 2

 

Lets find a value for angle3 +angle 4 now:

our original equation: angle 2+angle 3+angle 4=180

lets get rid of angle 2 the same way we did for the first equation by subtraction:

angle 3 and angle4= 180-angle 2

 

Now lets look at our 2 new equations:

angle 1= 180-angle2

angle3+angle 4= 180-angle 2

 

Notice they both have the same value! Now we can use substitution to prove they have the same value.

 

to recap we use our given information (always start off with the given information in a proof)

we define "linear pair"

we create equations showing our given information

we simplify the equations to find values for the measure of angle 1 and the measure of angle 3+4

then we use substitution to prove they are the same.